Answer:
a) For this case the random variable X follows a hypergometric distribution.
With parameters N=15, M=6 n =5
Where N=15 is the population size, M=6 is the number of success states in the population, n=5 is the number of draws, k is the number of observed successes
b)
We can find the individual probabilities:
And we got:
c)
And the deviation would be the square root of the variance:
Step-by-step explanation:
Previous concepts
The hypergeometric distribution is a discrete probability distribution that its useful when we have more than two distinguishable groups in a sample and the probability mass function is given by:
Where N=15 is the population size, M=6 is the number of success states in the population, n=5 is the number of draws, k is the number of observed successes
The expected value and variance for this distribution are given by:
a) What kind of a distribution does X have? (name and values of parameters)
For this case the random variable X follows a hypergometric distribution.
With parameters N=15, M=6 n =5
b) Computer P(X=2), P( X<=2), P(X>=2)
Using the pmf we have this:
For
We can find the individual probabilities:
And we got:
For the last case we can do this using the complement rule
Part c
The expected value and variance for this distribution are given by:
And the deviation would be the square root of the variance: